Nasal cannula harnesses which are employed to administer gases, such as oxygen, to the nasal passages of a patient, often require a relatively expensive nasal cannula. For example, a nasal cannual may include a hollow molded bridge member having integrally molded narine tubes and with the bridge member connected to a pair of gas supply tubes. Such hollow bridge members are relatively expensive to mold. In some cases, narine tubes are inserted through holes in a tubular bridge member. With the latter type of bridge, the narine tubes are generally not securely held against relative movement and bending so that there is a possibility that administration gas may be interrupted if a tube becomes bent in use. Also, such a tubular bridge member may become so flexible that the narine tubes are difficult to manage or be inserted and maintained within the nares of the patient.